Method for performing bistatic radar functions

ABSTRACT

A bistatic radar system having a transmitter that generates unique signals at spatially independent transmitter degrees of freedom and a receiver that filters the signal at each receiver degree of freedom into a group of signals identical in number to the number of transmitter degrees of freedom. The receiver formats the filtered signals into a 2-dimensional array of elements. The receiver rotates the array so that the new axes are aligned with the Doppler gradient. The data is then re-sampled and projected to linearize the clutter signal. The receiver may be integrated with a broad class of adaptive and non-adaptive clutter mitigation approaches such as electronic clutter tuning and projected bistatic space-time adaptive processing, or STAP.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of U.S. applicationSer. No. 11/103,128 filed on Apr. 11, 2005, now U.S. Pat. No. 7,038,618and claims the benefit of the filing date of such application.

This application claims the benefit of U.S. Provisional Application Ser.No. 60/565,376 filed on Apr. 26, 2004 by inventor Robert Budic.

Other related patent applications include the following:

“Adaptive Broadcast Radar,” U.S. Provisional Application Ser. No.60/253,095; Filed on Nov. 28, 2000; Inventor: Robert D. Budic.

“System and Method for Adaptive Broadcast Radar System,” U.S. Pat. No.6,861,976, issued Mar. 1, 2005; Inventor: Robert D. Budic.

The entirety of each of the aforementioned patent applications isincorporated by reference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to techniques for performing bistatic radarfunctions when a transmitter platform is in motion.

2. Brief Description of the Related Art

Radar systems may be monostatic, bistatic or multistatic systems.Monostatic radar systems consist of a transmitter and receiver that arecollocated on the same platform. A bistatic radar system performs radarfunctions but does not require the transmitter and receiver to becollocated. A multistatic radar system has multiple receivers that areseparated from one transmitter or one receiver that is separated frommultiple transmitters or multiple receivers that are separated frommultiple transmitters. Such transmitter and receiver platforms may bestationary (ground-based) or may be in motion.

A transmitted radar signal is scattered by all material objects.Knowledge of the transmitted signal is desirable at the receiver ifinformation is to be extracted from the target path signal. The strengthof the scattered signal is determined by the direction and orientationof the source relative to the radar antenna beam directions, by thedistances from the radar to the source, by electromagnetic properties ofthe source and the electromagnetic properties of the transmitter andreceiver hardware. A time or phase reference is desired if the totalscattered path length is to be determined. The transmitted frequencyalso is desired to determine the Doppler frequency shift. In a bistaticor multistatic system, the time reference also may be obtained from thedirect path signal provided the distance between the transmitter and thereceiver is known. The frequency reference may be obtained from a directpath signal received from the transmitter provided the transmitter andreceiver velocities are known.

The material objects that scatter the transmitted signal define amultipath environment. The multipath environment will, in general,include objects that are of interest to the radar operator as well asobjects that are not of interest. Those objects of interest in themultipath environment are called targets. Those objects that are not ofinterest are called clutter. Ground clutter refers to the multipathsources on the earth's surface and includes both natural vegetation andman-made structures. Ground clutter is often modeled as stationary, butdoes include motion due to the rotation of the earth and may haveinternal motion, such as due to wind. Ground clutter may also includesurface vehicles, animals or people and may be non-stationary due tomotion from one point to another during the period that the radar isoperating.

Decisions about the presence of a target of interest are calleddetection decisions. Detection decisions are based on the outputproducts of algorithms that process the radar signal.

Known radar systems may transmit a signal beam in a specific directionto search for targets. Once a target has been detected, a beam ormultiple beams may be directed to follow the target. The receiver mayreceive scattered signals reflected off the target. By knowing thetransmitter beam parameters, the receiver may perform operations todetermine the target parameters, as discussed above.

The performance of a radar system is characterized by its capability toreliably detect targets of interest while maintaining a low false alarmrate and by its capability to derive accurate estimates of targetposition and motion. For some radar systems, performance may be furthercharacterized by the capability to classify or identify the target ofinterest.

Radar measurements are derived from the received radar signal.Measurements commonly include signal strength, delay, Doppler and angleof arrival. Delay corresponds to the propagation time from transmitterto scatterer and back to receiver. Doppler corresponds to the shift infrequency of the scattered signal relative to the transmitted signal.The angle of arrival refers to the direction from the radar antenna tothe scatterer relative to the boresight direction of the antenna.

Measurements may be computed prior to, simultaneously with or afterdetection decisions. Algorithms may be applied to measurements to deriveestimates of the location and motion of a scattering source.

An ideal radar scenario is one for which the roll, yaw and pitch of theradar platform can be ignored, one for which radar hardwareimperfections such as array mis-alignment can be ignored and one forwhich clutter motion, clutter inhomegeneity and jammers can be ignored.

The cone angle is the angle between the radar platform heading and avector from the platform to a clutter sample. For linear side-lookingarrays, the azimuth angle is defined as π/2−θ_(cone)

The clutter locus describes the simultaneous measurement of Doppler andthe sine of the cone angle for clutter samples distributed over theradar field of view (FOV). The clutter locus depends on the radar systemand the clutter environment. For a selected ideal radar system, theclutter locus associated obtained for a selected radar scenario iscalled the Characteristic Clutter Locus.

A display of a Characteristic Clutter Locus for an ideal monostaticradar is shown in FIG. 1. The space-time aperture represents thesimultaneous measurement of Doppler and the sine of azimuth angle ofarrival. FIG. 1 shows the distribution of clutter measurements in thespace-time aperture for typical airborne radar. The clutter includessources that are spread over multiple range cells. The Doppler of aclutter sample depends directly on the azimuth of the clutter samplerelative to the platform.

The Characteristic Clutter Locus for an ideal monostatic radar islinear. The slope of the linear clutter locus depends on the magnitudeof the platform velocity and the orientation (θ₀) of the array relativeto the platform motion.

The slope of the Characteristic Clutter Locus for an ideal monostaticradar is delay independent. When ambiguous sidelobe returns areincluded, the Characteristic Clutter Locus will be a set of equallyspaced lines each with the same slope.

The performance of a radar system can be compared to a notional systemin which clutter is not present. The difference between the receivedsignal in an actual radar system and the notional radar system is calledthe clutter signal. The difference in performance between a radar systemand the clutter-free radar system in which clutter is not present iscalled the degradation in performance due to clutter. The clutter signalis treated as one type of interference that degrades radar systemperformance.

The radar system performance may be also be degraded by a component ofthe transmitted signal which propagates from the transmitter directlyinto the receiver system without scattering by the multipathenvironment. This is a second type of interference and called directpath interference.

A third type of interference is due to transmitters that operate eitherintentionally or unintentionally at or near the radar center frequency.Transmitters that operate intentionally at or near the radar centerfrequency are called jammers. Transmitters that operate unintentionallyare called co-channel transmitters. The interference signal due tojammers and co-channel transmitters may also include the effect ofscattering by the multipath environment.

For monostatic radars, pulsed waveforms have been traditionally used byradars to mitigate direct path interference.

For monostatic radars, adaptive antennas have been developed to suppressthe direct path component of jammer and co-channel interference sources.Adaptive antenna technology requires a radar antenna that has multiple,independent channels. Independent spatial channels may be derived fromthe output of distinct elements in a phased array, from the output ofdistinct sub-arrays that are created as a combination of feeds orelements or from separate antenna beams formed as a combination ofweighted data at the output of antenna elements or feeds. The technologyto form sub-arrays or multiple beams can be embedded in the design ofthe antenna hardware or implemented as a module or modules in thedigital signal processor. It is adaptive in the sense that processingparameters depend on the interference signal. Adaptive antennatechnology has been developed for ground-based radars and for radars onmoving platforms.

For monostatic ground-based radars, moving target indication (MTI) andDoppler radar were developed to suppress the stationary ground clutterand improve the detectability of moving targets. For such a ground-basedradar, all clutter has zero-Doppler and is concentrated in a singleDoppler measurement cell. A filter designed to cancel zero-Dopplermeasurements has the effect of suppressing background clutter. As longas the target is not flying in a direction orthogonal to the radar'slook direction (in which case it is as zero-Doppler and is filtered outalong with the background clutter), the target signal passes through thefilter without significant attenuation or distortion and targetdetection is no longer strongly degraded by the presence of backgroundclutter.

In monostatic airborne and space borne radar systems, ground clutter isa greater challenge primarily because it is spread throughout a largeregion of the delay and Doppler measurement space. The spread of groundclutter is, in general, a direct result of the radar's platform motion.The ground clutter generates an interference signal that is distributedthroughout the measurement space and masks targets that might otherwisebe detectable.

Displaced Phase Center Aperture (DPCA) processing and Space-timeadaptive processing (STAP) were invented as a technique to suppressstationary ground clutter when monostatic radars are deployed on movingplatforms for the purpose of detecting moving targets.

DPCA sensor and processing parameters do not depend on the clutterenvironment and in this sense are non-adaptive or deterministic. DPCA isapplied to receiver data before detection processing and measurementestimation.

At the foundation of monostatic clutter suppression techniques such asSTAP is the observation that clutter can be discriminated from targetsignals, even when they occupy the same range and Doppler measurementcell. The Doppler of a clutter cell depends linearly on the cosine ofcone angle of the clutter relative to the platform heading.Conceptually, this linear relationship defines, for each Doppler cell, aunique cone angle associated with the clutter source. A moving targetfor which the velocity component in direction of the radar motion isnon-zero cannot have identical Doppler and cone angle measurements asthe clutter. The difference between target and clutter cone anglemeasurement increases as a function of the target velocity component inthe direction of the radar platform heading. The placement of a null inthe antenna pattern in the direction of the clutter source willeffectively eliminate clutter returns for that Doppler cell. Movingtarget returns may also be attenuated but this attenuation will be muchless than the attenuation of clutter for those targets with sufficientlylarge velocity component in the direction of the radar platform heading.Thus, the detectability of moving targets is improved. As the speed of atarget is reduced, the characteristics of the target signal will becomesimilar to the characteristics of the clutter signal and will besuppressed along with clutter.

The quantity, Minimum Detectable Velocity (MDV), characterizes thecapability of DPCA and STAP algorithms to detect slow-moving targets.Signal to Interference-Plus-Noise Ratio (SINR) compares the strength oftarget signals to the combined signal consisting of interference orclutter and noise. SINR Loss describes the characterizes the performanceof DPCA and STAP algorithms to a interference-free environment.

STAP improves performance in the presence of both clutter andinterference due to jammers or co-channel transmitters. STAP can furthercompensate for mismatch in the RF characteristics between antenna andreceiver subsystems for the independent radar phase centers.

The application of STAP algorithms to radar data requires a radarantenna, similar to that described for adaptive antennas, with multipleindependent channels or outputs.

Coherent digital signal processing is commonly used to filter eachchannel of received data, prior to STAP processing, into a set ofmultiple data streams that are naturally associated with multipathsources at approximately, the same delay. Each specific delay value andthe variation in the delay value of filtered clutter samples is termed adelay bin. The variation in the delay value depends on the signalbandwidth and is commonly referred to as delay resolution orequivalently the extent of the delay bin. The filtering of each channelof receiver data into delay bins is commonly called delay processing ormatched filter processing. The pulse repetition interval (PRI) definesthe segment of transmitted signal that is used to compute the matchedfilter output. The Pulse Repetition Frequency (PRF) is defined as theinverse of the PRI.

For waveforms designed as a repeating pulse train, the PRI correspondsto the interval between two successive pulses. For non-recurringwaveforms, the PRI is not naturally defined by the signal structure andcan be specified as an independent signal or processing parameter. Theextent of PRI in this case may be defined, for example, to ensure thatcertain MF performance measures are met. Performance measures mightinclude expected signal-to-noise ratio (SNR) or de-correlation due toexpected motion of scatterers during the PRI.

Coherent digital signal processing can also be used to filter eachchannel into a set of multiple data streams that are naturallyassociated with multipath sources at approximately the same delay and atapproximately the same Doppler shift. Each specific delay and Dopplervalue and the variation in the delay and Doppler value of filteredclutter samples is termed a delay-Doppler or measurement bin. Thevariation in the Doppler value depends on the duration of the coherentintegration interval and is commonly referred to as Doppler resolutionor equivalently the extent of the Doppler bin. The filtering of eachchannel of receiver data into delay-Doppler bins is commonly calleddelay-Doppler processing, ambiguity surface processing and complexambiguity function (CAF) processing. The coherent processing interval(CPI) defines the segment of transmitted signal that is used to computethe CAF output.

Degrees of Freedom (DOF's) correspond to data values at the output ofthe radar signal processor. A three-dimensional index is commonly usedto parameterize DOF's. The three-dimensional index identifies a uniquereceiver element called the spatial DOF, a unique PRI called theslow-time DOF and a unique delay bin called the fast-time DOF.

The number of spatial DOF's is represented by K, the number of fast-timeDOF's by M and the number of slow-time DOF's by N. The total number ofindependent DOF's is the product of temporal and spatial DOF's and isequal to K·M·N.

Statistical properties of the interference signal are described by thecovariance, R, between the spatial and temporal DOF's. The eigenvaluesand eigenvectors of the covariance provide an equivalent representationor basis for the statistical properties of the interference signal. Thenumber of eigenvalues/eigenvectors is equal to K·M·N, the number ofindependent DOF's. The order or rank of a covariance matrix is equal tothe number of eigenvalues/eigenvectors.

In some cases, it may be possible to describe the statisticalcharacteristics of clutter and other sources of interference by a lowerdimensional set of basis vectors. The rank of the clutter and/orinterference is defined as the number of basis vectors required for thisrepresentation. The rank of clutter or interference data may be lessthan the rank of the full covariance matrix.

For a monostatic radar scenario, the clutter rank may be significantlyless than the rank of the full covariance matrix. For an idealmonostatic radar scenario, fast-time DOF's are not required for cluttersuppression and M is typically set equal to 1. The clutter rank is anestimate of the number of significant eigenvalues. For an idealmonostatic radar scenario, the rank of the interference is approximatelyK+(N−1)β where β is a factor of 2 times the ratio of distance traveledby the radar platform during the time between radar pulses and theseparation between spatial DOF's. A measure of the rank reduction is theratio of K+(N−1)β to the product K·N.

The reduced rank of clutter is a direct consequence of the linearity ofthe clutter locus. This is commonly referred to as “Brennan's rule”.

The desired response for a STAP processor is defined by a space-timesteering vector, v.

The optimum STAP processor, w, depends on the covariance and theselected steering vector: w=R⁻¹ v. The computational complexity istypically dominated by the need to determine the inverse of thecovariance.

In practice, an estimate of the covariance for a selected delay bin isderived from data in neighboring bins. This data is referred to astraining data. The clutter rank for training data in an ideal monostaticscenario that is the same as the clutter rank for the selected delaybin. In addition, for an ideal monostatic scenario, the statisticalcharacteristics of covariance estimate based on training data aresimilar to that of the ideal covariance and when the amount of trainingdata is approximately twice the order of the covariance, the achievedperformance is roughly within 3 dB of that for the optimum STAPprocessor.

Because the both the computational complexity and the size of trainingdata increase with the order of the covariance, techniques to reduce therank or dimensionality of data at the input of the STAP processor arecommonly employed.

One class of techniques uses non-adaptive or deterministic processingand is referred to as subspace projection. Sub-space projectiontechniques include Post-Doppler STAP in which slow-time DOF's aredefined at the output of CAF processing. Staggered PRF, as an example ofPost-Doppler STAP techniques. For Staggered PRF, the slow-time DOF's aredefined by a sequence of over-lapping CPI's. Adjacent cell Post-DopplerSTAP is another example of Post-Doppler STAP techniques where slow-timeDOF's are derived from data in neighboring Doppler bins.

Sub-space projection techniques also include Beamspace STAP in whichspatial DOF's are reduced by application of a set of distinct, fixedaperture weights to the spatial DOF's and the summation of the weighteddata. The fixed aperture weights may be employed to form a set of fixed,overlapping radar beams where each radar beam has a unique beam center.The fixed aperture weights may also be employed to define overlappingsub-arrays where the phase centers of the set of sub-arrays arespatially separated. The formation of independent and distinct beams orsub-arrays for Beamspace STAP may be embedded in the design of theantenna hardware or implemented as a module or modules in the digitalsignal processor.

Post-Doppler and Beamspace STAP techniques can be employed separately orin combination as a STAP pre-processor such as for the Joint DomainLocalized Generalized Likelihood Ratio Detector (JDL-GLR).

Another class of techniques, Reduced Rank STAP algorithms, use adaptiveprocessing to exploit the fact that inherent dimensionality or rank ofclutter or may be significantly lower than the rank of the covariancematrix. Reduced Rank STAP algorithms include Principal Components,Eigenfilters and the Cross-Spectral Metric. Reduced Rank STAP algorithmsalso include Multi-stage Wiener Filters (MWF) and Parametric MatchedFilters (PMF) that do not explicitly require knowledge or estimation ofthe covariance. Reduced Rank STAP algorithms can also be combined withPost-Doppler and Beamspace techniques.

Diagonal loading and covariance matrix tapers can be employed tocompensate for internal clutter motion and clutter non-stationarity.

The inclusion of fast-time DOF's and a technique referred to as 3-D STAPhas been developed to suppress multipath scattering by a jammer. Thejammer multipath is commonly referred to as “hot clutter”.

Performance may also be enhanced by the inclusion of elevation DOF's inaddition to azimuth DOF's.

Analyses, simulations and experiments have demonstrated that theperformance achieved with partially adaptive STAP can approach that of afully adaptive STAP processor.

Performance of STAP algorithms may be described by a plot of the SINRLoss over the space-time aperture. For an ideal monostatic radar, theSINR Loss will be characterized by a sharp linear null that is alignedwith the clutter locus. The width of the null is a measure of MDV. Thewidth of the null depends directly on the selection of radar DOF's, theSTAP algorithm and signal processing parameters.

Differences in STAP algorithms are the result of the need to compensatefor the more complex signal environment in a practical system that mayinclude mismatch in receiver channels, roll, yaw and pitch of the radarplatform, jammers, clutter motion and clutter inhomogeneities.

In bistatic radar systems, the vectors from the transmitter to areference point, from the receiver to the same reference point and fromthe receiver to the transmitter define the sides of a triangle. Theincluded angle at the reference point is called the bistatic angle. Thebistatic angle measures the departure of a bistatic sensor frommonostatic operation. For monostatic radar the bistatic angle is zero.

Bistatic radar operation may enable improved detection performance.Unlike the transmitter, the receiver does not have a largeelectromagnetic signature and so can be located closer to targets ofinterest. The reduction in range translates into increasedsignal-to-noise ratio (SNR) and the potential to detect small targetsthat might fall below the noise level for a radar receiver co-locatedwith the illumination source (i.e., for monostatic operation).

Bistatic radar receiver operation may enable improved performance in thepresence of countermeasures. Because bistatic receivers are passive,electronic countermeasure systems designed to determine the location ofa receiver and direct jammer energy toward it are reduced ineffectiveness. Similarly, radar cross-section reduction technologydesigned to re-direct scattered energy away from the transmitter arereduced in effectiveness.

Similarly, passive operation at reduced ranges may enable covert andclandestine deployment throughout an area of interest.

Multiple bistatic radar receivers can simultaneously exploit a singleradar transmitter. This mode of operation is one example of multistaticoperation and can be used to mitigate the effect of radar cross-sectionfluctuations and/or multipath fading and improves performance comparedto monostatic radar.

The linearity of the clutter locus is retained in certain bistatic radarsystems, those for which the transmitter is stationary. In such asystem, there is no Doppler on the transmitter to clutter propagationpath and the Doppler on the clutter-to-receiver propagation is just ½ ofthat for a monostatic radar system. In addition, the slope of theclutter locus is range independent. Because of the range independence,characteristics of clutter in a given range cell, i.e., R, thespace-time covariance of clutter measurements, can be estimated based ondata in neighboring range cells. The clutter suppression filter can thenbe derived in terms of the estimated clutter covariance.

FIG. 2 shows 4 delay strips for a typical airborne bistatic scenario anddemonstrates that very basic relationships are simply lost in a bistaticsystem when the transmitter and receiver motion are unconstrained. Forthe scenario shown in FIG. 2, the transmitter is heading Northeast witha speed of 180 km and the receiver is approximately 140 km Southeast ofthe transmitter. Lost are linear and invariant relationships betweenspace-time sensor measurements, specifically, the linear and delayinvariant relationship between Doppler and sine of the azimuth angle,relationships that are the basis for clutter and interferencesuppression technology in monostatic systems.

Current bistatic and multistatic radar designs design and derive DOF'sthat are similar to those in a monostatic radar. Current approaches tobistatics and multistatics, for example, view the transmitter as anindependent and essentially non-adaptive component of the larger system.Spatial degrees of freedom (DOF's) are allocated, in their entirety, tothe receiver. While adaptive signal processing including STAP iscommonly employed, the signal processing does not include transmitterfeedback or adaptation of the transmitter aperture.

Because bistatic and multistatic clutter is highly non-linear andnon-stationary, the direct application of STAP techniques developed formonostatic radar will have limited capability to suppress or cancelclutter while maintaining moving target detectability.

Approaches to bistatic and multistatic clutter suppression fall into twogeneral categories: 1) clutter tuning and 2) measurement compensation.

Clutter tuning refers to attempts to eliminate or minimize the need forclutter suppression and STAP processing. Clutter tuning effectivelyrestricts platform trajectories or restricts segment of platformtrajectories for which data is processed in an effort to minimize theregion of Doppler measurements containing clutter. For an ideal cluttertuning scenario, the transmitter and receiver platforms are at the samevelocity and are moving toward a common point. In this case, the Dopplerof clutter is exactly zero and the effects of clutter are highlylocalized in measurement space. The localization of clutter inmeasurement space is approximately obtained for transmitter and receiverplatform motion that departs from the conditions for ideal cluttertuning. A practical system based on clutter tuning requires, in general,an increased number of platforms to ensure detection of all targets.

Measurement compensation techniques typically invoke physical models todefine groups of similar scattering centers in neighboring delay topredict, for these scatterers, the dependence of the clutter locus ondelay, Doppler and/or angle. The delay, Doppler and angle measurementsof similar scattering centers define a map between neighboringmeasurement bins. This map can be used to identify and compensatemeasurements that are used to estimate the covariance of clutter or tootherwise characterize the statistical properties for techniques such asthe Multistage Wiener Filters that do not require explicit computationof the covariance, define a map between delay bins that identifies andto compensate for variation in Doppler and angle measurements.

Measurement compensation techniques include derivative based updating(DBU), Doppler compensation and Doppler-angle compensation. Measurementcompensation are designed for integration with STAP techniques developedfor monostatic radar.

A single preferred combination of measurement compensation and STAPtechniques has not been established. The special case of a bistaticradar with a stationary transmitter illustrates certain issues. TheCharacteristic Clutter Locus for a bistatic radar with a stationarytransmitter shares the same linear and delay independent characteristicsof the monostatic radar as shown in FIG. 1. However, when the strengthof the radar return is also taken into account, it is known that thepeak of the return will migrate along the linear clutter locus as thedelay bin is varied. It has been shown even though the clutter locus islinear and delay invariant, the performance of JDL-GLR STAP algorithmswill be significantly degraded unless the STAP algorithm is integratedwith angle-Doppler compensation. In contrast, the it has been shown thatParametric Match Filters (PMF) can achieve effective clutter suppressionwithout the integration of angle-Doppler compensation.

SUMMARY OF THE INVENTION

This invention provides the means to generate unique signals forspatially independent transmitter elements, for phase centers ofdistinct sub-arrays and for independent transmitter beams. The inventiondescribes waveform codes that enable the signal at each receiver DOF tobe filtered into a group of signals. The number of filtered signals isidentical to the number of transmitter DOF's. Each filtered signal isuniquely associated with a transmitter DOF and a receiver DOF.

The invention describes a technique for formatting the filtered signalsinto a 2-dimensional array of elements called the Generalized BistaticAperture and assigning one of the filtered signals to an element in theGeneralized Bistatic Aperture. The vertical position of the element in aGeneralized Bistatic Aperture is defined by the index of the transmitterDOF. The horizontal position of the element is defined by the index ofthe receiver DOF.

The invention describes a technique to filter the signal at each elementof the 2-dimensional Generalized Bistatic Aperture into a 1-dimensionalarray of signals. Each signal component in the 1-dimensional array isassociated with multipath sources in a unique delay bin. After delayprocessing, the filtered signals are described by a 3-dimensional indexthat associates each filtered signal component with a unique transmitterDOF, receiver DOF and delay bin. An independent 3-dimensional array offiltered signals will be derived from data collected over an interval oftime, called the dwell. The 3-dimensional index is extended to4-dimensions by adding an index that identifies the dwell of thereceived data.

The 4-dimensional data arrays are called Fully Adaptive Data Quads.

The invention describes an alternate technique to filter the signal ateach element of the 2-dimensional Generalized Bistatic Aperture into a2-dimensional array of signals. Each signal component in the2-dimensional array is associated with multipath sources in a uniquedelay-Doppler bin. After delay-Doppler processing, the filtered signalsare described by a 4-dimensional index that associates each filteredsignal component with a unique transmitter DOF, receiver DOF, delay binand Doppler bin. An independent 4-dimensional array of filtered signalswill be derived each CPI. The 4-dimensional index is extended to5-dimensions by adding an index that identifies the CPI of the receiveddata. For each Doppler index, the data spans a 4-dimensional sub-spacethat is similar in structure to the 4-dimensional data structure definedin the above paragraph.

The 4-dimensional index that is derived can also be extended to5-dimensions by adding an index that identifies neighboring Dopplerbins. For each Doppler index, the data spans a 4-dimensional sub-space.

The 4-dimensional data arrays are called Partially Adaptive Data Quads.

The Fully Adaptive and Partially Adaptive Data Quads can be factoredinto 2 orthogonal 2-dimensional sub-spaces. The first of the2-dimensional sub-spaces spans the Generalized Bistatic Aperture. Thesecond spans temporal measurements. The temporal measurements aredelay-time for the Fully Adaptive Pre-processor and delay-time ordelay-frequency for the Partially Adaptive Pre-processor.

The generalized bistatic clutter locus, defined as the locus ofsimultaneous Doppler-Transmitter Angle-Receiver Angle measurements in aselected delay bin. For an ideal bistatic radar that incorporates thisinvention, the generalized bistatic clutter locus is called theCharacteristic Clutter Locus for DBA. The Characteristic Clutter Locusfor DBA is constrained to a plane in the 3-dimensional measurementspace. For an ideal bistatic radar that incorporates this invention theplane is independent of delay bin.

The invention describes techniques to reduce the size of the trainingdata set for sensor data with a generalized bistatic clutter locus thatis constrained to a plane. The first technique rotates and projects the2-dimensional Generalized Bistatic Aperture subspace into a1-dimensional linear array. The data at each element in the rotated andprojected array is a linear combination of filtered signals. Afterrotation and projection, the 4-dimensional data arrays are transformedinto 3 dimensional sub-arrays, called Generalized Bistatic STAPDatacubes, with 1 spatial and 2 temporal dimensions.

The invention describes a technique to interface the GeneralizedBistatic STAP Datacubes to clutter suppression algorithms that have beendeveloped for monostatic radar.

The invention describes an alternate technique based on MultistageWiener Filters to simultaneously reduce the size of training data setsand suppress clutter.

In one embodiment of the invention, a transmitter for a bistatic radarsystem comprises a programmable waveform generator for creating an arrayof multiple independent waveforms and a plurality of RF sections fortransmitting said independent waveforms, wherein each RF sectiontranslates the array of waveforms from IF to RF, amplifies the array ofwaveforms, and uses phase shifts and channel weighting to shape andsteer a transmitter beam of the array of waveforms.

Another embodiment of the invention comprises a method of filtering andprocessing a received radar signal comprising the steps of: receiving anelement-level radar signal; splitting the element-level radar signalinto a plurality of signal components, each signal component comprisingenergy scattered by a specific transmit element—receiver—element pair;forming a 2-D array of data associated with a plurality of transmitterand receiver degrees of freedom; rotating the 2-D array of data;re-sampling the array of data to find new degrees of freedom; and usinga projection to eliminate residual degrees of freedom.

In yet another embodiment of the invention, a bistatic radar receiversensor comprises a transmit aperture expansion on receive module; abistatic aperture compression module; and a clutter mitigation module,wherein the transmit aperture expansion on receive module comprises:means for decomposing a received signal into signal component dataassociated with transmit-receive array element pairs; and means fororganizing said signal component data into a two-dimensional array. Thebistatic aperture compression module may comprise means for rotating thetwo-dimensional array.

Aspects, features, and attendant advantages of the present inventionwill become apparent to those skilled in the art from a reading of thefollowing detailed description of embodiments constructed in accordancetherewith, taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention of the present application will now be described in moredetail with reference to preferred embodiments of the architecture andmethod, given only by way of example, and with reference to theaccompanying drawings, in which:

FIG. 1 illustrates the clutter measurements in a space-time aperture fora typical airborne monostatic radar system.

FIG. 2 illustrates 4 delay strips for a typical bistatic radar system inwhich the transmitter is moving.

FIG. 3 is a diagram of a distributed bistatic aperture system inaccordance with an embodiment of the present invention.

FIG. 4 is a block diagram of transmitter in accordance with anembodiment of the present invention.

FIG. 5 is a functional block diagram of the waveform generator of atransmitter in accordance with an embodiment of the present invention.

FIG. 6 shows a functional block diagram of a distributed bistaticaperture receiver in accordance with an embodiment of the presentinvention.

FIG. 7 illustrates a receiver sensor architecture for a distributedbistatic aperture system in accordance with an embodiment of the presentinvention.

FIG. 8 illustrates a block diagram of a transmit aperture expansion onreceive module for a distributed bistatic aperture system in accordancewith an embodiment of the present invention.

FIG. 9 illustrates a functional block diagram of a bistatic aperturecompression module in accordance with an embodiment of the presentinvention.

FIG. 10 a shows a coordinate system for steering vectors an impulseresponse for a vertical or transmitter steering vector displaced alongthe transmitter axis in accordance with an embodiment of the presentinvention.

FIG. 10 b shows an impulse response for a horizontal steering vectorsample.

FIG. 11 a shows the phase response of a steering vector over theK_(tx)×K_(rx) phase centers in a Generalized Bistatic Aperture.

FIG. 11 b shows a phase response corresponding to FIG. 11 over aGeneralized Bistatic Aperture.

FIGS. 12 a-b show the displacement of steering vector samples along eachof the two independent axes.

FIGS. 13 a-b show the phase response associated with each of the twosteering vector samples of FIGS. 12 a-b.

FIG. 14 is a block diagram of a clutter mitigation system in accordancewith an embodiment of the present invention.

FIGS. 15 a-b show the results of example simulations that demonstrateperformance capabilities that are obtained with this invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention of distributed bistatic apertures builds on basicprinciples and reformulates the bistatic clutter suppression problem ina way that desirable features of monostatic operation, linearity anddelay-independence, re-emerge. In particular, this new approach beginswith the observation that the temporal clutter signature, the Dopplershift, is inherently distributed in space-time in the sense that it isdepends on a combination of transmitter and receiver motion and positionof the clutter patch relative to both the transmitter and receiver. Thisbeing the case, a simplified linear coupling with angle measurementswill emerge only when the bistatic aperture is expanded to includetransmitter degrees of freedom. When this is accomplished, the anglemeasurements, measurements of the spatial signature (i.e., sensorDOF's), are also distributed and more naturally matched to the observedDoppler effects.

FIG. 3 depicts an example of an environment of an adaptive radar systemfor detecting and tracking a target in accordance with the presentinvention. A transmitter such as space borne transmitter 310 emitswideband electromagnetic energy transmissions in all directions. Thetransmitter 310 may include a plurality of elements and may be a phasedarray. Alternatively, the transmitter 310 may include a plurality ofsub-arrays with spatially distinct phase centers. Alternatively, thetransmitter 310 may include multiple beams with distinct beam centers.The signal may comprise orthogonal or pseudo-orthogonal signals.

Some of such transmitted signals are scattered by targets 320, 330. Thescattered signals from target 330 may be received by space-bornereceiver 350 or by airborne receiver 340 or by a ground receiver (notshown). At the receiver 350, the receiver element signal is decomposedinto transmitter element components 360. The receivers 340 and 350 maycomprise different components and may be an phased array of receiverelements or an array of sub-arrays or multiple beam antennas.

A distributed bistatic aperture (“DBA”) creates spatial transmitterDOF's. Transmitter DOF's are formed as independent, spatially separatedsub-arrays in the transmitter array or as simultaneous, independentbeams. Unique waveforms are emitted through the phase center for eachDOF.

The present invention introduces a new type of transmitter thatincorporates a new approach to radar waveform design. The waveformdesign approach is built upon communications technology and provides forsharing of radar bandwidth among transmitter DOF's. These codes provideorthogonality or approximate orthogonality between channels in thepresence of multipath (e.g., clutter).

The family of dual waveforms is replicated at the receiver and used tofilter the signal at the output of each receiver element or sub-array.The filtering operation splits the element-level received signal intocomponents. After filtering, the signal components contain the energyscattered by a specific transmit element—receive-element pair. A 2-Darray of data associated with transmitter and receiver DOF's is thenformed.

FIG. 4 illustrates an embodiment of a DBA transmitter in accordance withthe present invention. FIG. 5 shows the functional block diagram for anexample waveform generator 410 called the Vandermonde-LaGrange (LV)Waveform Generator. At the core of the LV Waveform Generator 410 is theBaseband Signal Generator 412 that computes the time samples for whatcorresponds to a radar pulse. The waveform generator includes optionsfor reference pulses based on impulse, Linear FM (LFM), and Pseudo-Noise(PN) modulation. Bandwidth, duration, duty factor and pulse shaping(e.g., uniform or Taylor weighting of the time series) are userspecified parameters.

The output of the Baseband Signal Generator 412 is termed a referencepulse. A comb filter 414 is then applied to generate a referencewaveform that retains the correlation properties of the reference pulsewhile reducing its spectral content. The comb filter 414 implementationsimply generates a coherent repetition of the reference pulse. Thespectrum of the pulse train is effectively zero, except at a set ofequally spaced frequencies, and, at those frequencies, the spectrum ofthe pulse train is equal to that for the baseband waveform. Theseparation of spectral samples, Δf, is equal to the inverse of theinter-pulse interval, τ_(p), (or, for waveforms with a unity dutyfactor, the pulse duration). The width of the spectral samples is equalto the inverse of the duration of the reference waveform.

The coded LV waveforms are derived from the reference waveform (i.e.,from the coherent pulse train). To accomplish this, for an N channeltransmitter, the LV pole generator 416 divides the interval betweenspectral samples into N intervals. For this example waveform generator,the interval is divided into equally spaced intervals with separationΔf_(ch). Typical values for Δf_(ch) are on the order of 100's of Hz to10's of kHz. Then, for each of the transmitter channels, a sub-carrieris generated at a multiple of Δf_(ch). The N sub-carriers are thenapplied to replicas of the reference pulse train. By convention, thesefrequency shifts 418 are positive and the frequency shift is anup-conversion. The up-converted pulse train represents the LV waveform.

The waveforms for each of the transmitter channels overlap in thetemporal domain and are interleaved in the spectral domain. Thisapproach enables the use of continuous reference waveforms andtransmitter signals with unity duty factor.

The frequency offset between channels is a fraction, Δf_(ch)/B_(signal),of what would be required for conventional frequency divisionmultiplexing (FDM). The LV codes are coherent or approximately coherentin the sense that transmitter angle information is preserved and theaccuracy of transmitter angle measurements derived at the receiver fordistributed sources increases as the ratio Δf_(ch)/B_(signal) decreases.For FDM, this ratio is unity (or larger) and transmitter anglemeasurements are not accurately related to the bearing of distributedsources relative to the transmitter. In this sense, FDM signals do notmaintain coherence in the presence of distributed multipath.

More generally, a family of reference pulses might be built on family ofphase-coded pulses. Phase coding may be used to eliminate frequencychannel offsets and thereby improve the code coherence. Further, thePulse Repetition Frequency (PRF) for each pulse in this set may bevaried.

The DBA transmitter shown in FIG. 4 locks all frequencies and timingsignals to a common stable oscillator. The programmable DBA waveformgenerator 410 creates an array of multiple, independent waveforms thatare then fed to identical RF sections, one for each transmitter phasecenter. The signal generator will also provide any requiredchannel-to-channel amplitude weighting. The RF section translates thearray of DBA waveforms from IF to RF at mixers 420 and provides poweramplification 430. Programmable RF phase shifts 440 at each phasecenter, combined with channel-to-channel weighting can be used to shapeand steer a nominal transmitter beam. In the default mode, whenchannel-to-channel waveforms are identical, the complex aperture weightscontrol the transmitter sidelobe levels and beam direction.

FIG. 4 also shows an independent, “direct path” channel. This isincluded to ensure that any DBA receiver will, in general, have thecapability to recover the reference phase of any transmitter that is tobe exploited. The DBA receiver similarly may have a relatively low-gainreference aperture, aimed at the transmitter, with a signal processingchain designed to regenerate the reference RF phase.

FIG. 6 shows the primary RF components of the DBA receiver. A referencereceiver 602 receives the direct path signal and provides the signal toa controller 608 and a reference oscillator 604. The referenceoscillator 604 provides its output to the timing unit 606 and aplurality of mixers 612. A plurality of high dynamic range receivers 610receive the radar signals. The use of coherent high dynamic rangereceivers 610 is preferred because leakage of the transmitter signalthrough transmitter and receiver sidelobes will often be the dominantsignal component and a source of receiver phase noise. The referenceoscillator 604 and timing unit 606 are locked to the direct path signalreceived at reference receiver 602. Channel-to-channel coherency ofreceived data streams can be accomplished by locking all localoscillators to the reference oscillator 604. FIG. 6 shows that thisreference oscillator 604 is driven by the direct path signal. Thisprovides coherency between transmitter and receiver channels.

The output of the receiver is an array of digitized data channels thatcorrespond, on a one-to-one basis, with the spatial samples of scatteredsignals at the array of receiver phase centers.

FIG. 7 shows an embodiment of a receiver sensor processor forDistributed Bistatic Apertures. The block diagram shows three primarymodules, Transmit Aperture eXpansion On-Receive (TAXO-R) 710, BistaticAperture Compression (BAC) 720 and Clutter Mitigation processing 730.

The TAXO-R module 710 implements the decomposition of the receivedsignal into components associated with transmit-receive array elementpairs. It is built on an array of matched filters 712, one signal 714for each receiver element. Each of the element-level filters shown inFIG. 7 is itself an array of matched filters based on the array of codedtransmitter signals. The filtering can be performed on a single pulse(delay-only filtering) or a group of pulses (delay-Doppler filtering).The signal 718 from the mth Transmit—nth Receive element pair isprovided from the matched filters 712 to the Format Aperture Data module716. The ‘Format Aperture Data’ module 716 organizes the signalcomponent data into a 2-dimensional array of data channels, with thevertical axis used to specify transmitter array element number and thehorizontal axis used to specify receiver array element number. Thenumber of complex samples along the vertical axis is equal to the numberof transmitter DOF's, K_(tx). The number of complex samples along thehorizontal axis is equal to the number of receiver DOF's, K_(rx). Thenumber of complex samples in the Generalized Bistatic Aperture is:K_(TAXOR)=K_(tx)×K_(rx) The result of the TAXO-R module 710 is anincrease in sensor degrees of freedom from K_(Rx) at 714 to K_(TAXOR) atthe output of 716 and 710.

The aperture response (also known as the impulse response and pointspread function) describes the change in gain as a sample point isdisplaced from a reference point by the amount δ x _(p). The transmitter[receiver] aperture response for this invention is denoted H^(TX[RX])and depends on:

-   -   a. the signal wavelength, λ,    -   b. the signal bandwidth, B_(signal),    -   c. the channel offset, Δf_(ch),    -   d. the delay resolution, Δ_(res)    -   e. the number of transmitter [receiver] phase centers:        K_(TX[RX])    -   f. the displacement between transmitter [receiver] phase        centers: d _(TX[RX])    -   g. the direction vector between the transmitter [receiver] and        the reference point: ê_(p) ^(TX[RX])    -   h. a cross-range vector that is orthogonal to the transmitter        [receiver] direction vector: û_(p) ^(TX[RX])    -   i. the distance from the transmitter [receiver] to the reference        point: ρ_(p) ^(TX[RX])

For uniformly weighted apertures, the receiver aperture response ismodeled as:

$H^{\lbrack{RX}\rbrack} \equiv {\sin\;{{c\left( {K_{RX}\left\lbrack \frac{\left( {\delta\;{{\overset{\_}{x}}_{p} \cdot {\hat{u}}_{p}^{RX}}} \right)\left( {{\overset{\_}{d}}_{RX} \cdot {\hat{u}}_{p}^{RX}} \right)}{\lambda_{\mu}\rho_{p}^{RX}} \right\rbrack} \right)}.}}$

For uniformly weighted apertures, the transmitter aperture response ismodeled as:

$H^{\lbrack{TX}\rbrack} \equiv {\sin\;{{c\left( {K_{TX}\begin{bmatrix}{\frac{\left( {\delta\;{{\overset{\_}{x}}_{p} \cdot {\hat{u}}_{p}^{TX}}} \right)\left( {{\overset{\_}{d}}_{TX} \cdot {\hat{u}}_{p}^{TX}} \right)}{\lambda_{\mu}\rho_{p}^{TX}} +} \\{\left( \frac{\Delta\; f_{ch}}{B_{signal}} \right)\frac{\delta\;{{\overset{\_}{x}}_{p} \cdot \left( {{\hat{e}}_{p}^{TX} + {\hat{e}}_{p}^{RX}} \right)}}{\Delta_{res}}}\end{bmatrix}} \right)}.}}$

This receiver aperture response shows that the receiver gain decreasesas the cross-range displacement increases.

For the transmitter aperture response, the first argument in the sincfunction is analogous to that for the receiver aperture response anddescribes gain for points near the beam center. The second termdescribes a focusing of the aperture response in the direction, (ê_(p)^(TX)+ê_(p) ^(RX)), that is parallel to the gradient of the delaymeasurement. When Δf_(ch)□B_(signal), this term is negligible and thetransmitter measurements are combined to form a transmitter beam. Inthis regard, when Δf_(ch)□B_(signal), the transmitter measurements andDOF's are coherent.

When Δf_(ch)□B_(signal), the transmitter DOF's are combined toeffectively increase the signal bandwidth and improve delay measurement.As a result, when Δf_(ch)□B_(signal), the information associated withangle measurement relative to the transmitter cannot be derived andcoherence is lost.

The Bistatic Aperture Compression (BAC) or Pre-processor module 720follows the TAXO-R module 710. While the TAXO-R module 710 serves toexpand the degrees of freedom and ensure that those required forlinearity are included, the BAC module compresses or eliminates thosedegrees of freedom that are not required for clutter linearity. The BACmodule, in combination with the TAXO-R module, serves as a cluttermitigation preprocessor, one designed to find and then minimize thedegrees of freedom that govern clutter linearity.

The BAC module 720 first rotates DOF's for the TAXO-R array viacoordinate rotating means 722 so that the new axes are aligned with theDoppler gradient. The array data is re-sampled at the re-sampler means724 to ensure that it is aligned with the coordinate grid of the rotatedcoordinates.

After rotation and re-sampling, a projection module 726 is used toeliminate the residual degrees of freedom, i.e., those which areorthogonal to the Doppler gradient and are not needed for linearization.After rotation, re-sampling and projection, the clutter is linearizedand the degrees of freedom are reduced.

FIG. 8 shows a more detailed functional block diagram for an embodimentof the TAXO-R signal processor or module of the present invention. TheTAXO-R signal processor operates independently on each of the receiverdata channels and is designed to de-multiplex the received signal intochannels where each channel includes only a single LV waveform (from thek^(th) transmitter channel) and all associated multipath components. Theoutput of the TAXO-R signal processor is a set of ambiguity surfaces(a.k.a., CAF's or delay-Doppler surfaces), one for each slow-time DOFand each transmitter-receiver phase center pair.

The input signal for the k^(th) receiver channel is a composite signal810. That is, each of the coded transmitter signals, together with allthe delay and Doppler shifted multipath components are combined at anyselected receiver phase center. FIG. 8 shows use of the DBA WaveformGenerator 820 having a baseband signal generator 822 and an offsetfrequency generator 824 to create replicas of the transmitted signal.Alternate configurations include generation of the reference waveformfrom the direct path signal. Motion Compensation (MOCOMP) module 830applies motion compensation to the direct path signal to compensate forphase variations tied to platform motion and displacement of transmitterphase centers. MOCOMP module 830 is also used to remove from eachreceiver channel the overall phase variations due to sensor motionrelative to a reference point called the scene center. The receiverchannel is offset in frequency to compensate for offset of each selectedtransmitter channel. The compensated direct path and receiver signalsare input to a CAF processor, implemented as a Matched Filter 840cascaded with a Doppler Filter 850. A channel-selection filter 860centered on zero-Doppler extracts the clutter response for the selectedtransmitter channel.

For certain bistatic radar scenarios, the delay of multipath source atscene center, τ_(sc) may be larger than the PRI. For these scenarios,the channel selection filter 860 applies a linear phase shift, Δφ_(k)across each group of transmitter DOF's. The order of the ambiguity,N_(amb) is defined as

$N_{amb} = {{floor}\mspace{11mu}\left( \frac{\tau_{SC}}{PRI} \right)}$The linear phase shift applied at 860 to a group of transmitter DOF's(indexed by k) in the channel selection filter 860 isΔφ_(k)=2π(k−1)Δf_(ch)N_(amb)PRI.TAXO-R data at output of 860 is a set ofK_(TAXOR) vector samples, IQ, for each delay-Doppler measurement cell.

FIG. 9 shows a functional block diagram of an embodiment of a BistaticAperture Compression (BAC) module in accordance with the presentinvention. BAC is a process designed to isolate DOF's associated withclutter linearity and then to compress the dimensionality of TAXO-Rdata, removing those DOF's that are not tied to clutter linearity. Aby-product of BAC processing is a set of steering vectors for ClutterMitigation Processing.

The BAC module computes a rotation angle at 910 that is used to mixtransmitter and receiver DOF's. The rotation angle is defined in termsof the speed of the transmitter, |V_(TX)|, the speed of the receiver,|V_(RX)|, the spatial separation of transmitter DOF's, d_(TX) and thespatial separation of the receiver DOF's, d_(RX). A specific form forthe desired rotation angle is as follows:

$\phi_{DBA} = {\tan^{- 1}\left( {\frac{V_{Tx}}{V_{Rx}} \cdot \frac{d_{Rx}}{d_{Tx}}} \right)}$

The rotation angle, Φ_(DBA), is used to compute a coordinate grid forspatial steering vectors at 920. The computation begins with an initial2-dimensional coordinate grid, GRID−SV_(φ=0), where the x-dimensioncorresponds to the sine of the receiver azimuth angle measurements,sin(θ_(Rx)) and the y-dimension corresponds to samples of the sine ofthe transmitter azimuth angle measurements, sin(θ_(Tx)). The initialgrid is rotated though the angle, Φ_(DBA). The axes for the rotatedgrid, GRID−SV_(φ=φDBA), are denoted x′ and y′. Each value on the x′ axisdefines a unique pair of transmitter and receiver measurements:[sin(θ_(RX)),sin(θ_(TX))]

The pair of transmitter and receiver measurements define a pair oftransmitter and receiver steering vectors SV _(TX) and SV _(RX). Thesteering vector for the selected point on the x′ axis is computed at 930as the product of the transmitter and receiver steering vectors. The setof steering vectors defined by samples along the x′-axis are called“horizontal steering vectors” 932. In a similar manner steering vectorsare computed at 930 for samples along the y′-axis. The set of steeringvectors defined by samples along the y′-axis are called “verticalsteering vectors” 934. Horizontal steering vectors 934 are denoted: SV_(horiz). Vertical steering vectors 932 are denoted: SV _(vert). Ageneral steering vector can be derived as a product of vertical andhorizontal steering vectors.SV= SV _(horiz) · SV _(vert)

The rotation angle is used to compute a projection operator, π, at 940.The computation of the projection operator begins with the definition ofa 2-dimensional coordinate grid for the Generalized Bistatic Aperture.The coordinates correspond to indices assigned to the transmitter andreceiver DOF's. Receiver coordinates are aligned with the x-axis andtransmitter coordinates are aligned with the y-axis. A rotation throughthe angle Φ_(DBA) as defined above is applied to the GeneralizedBistatic Aperture coordinates. After the rotation, data values will, ingeneral, not be associated with integer values of the rotatedcoordinates. Interpolation is used to map data values for theGeneralized Bistatic Aperture into a new set of values defined atinteger values of the rotated coordinates. This process re-samples theGeneralized Bistatic Aperture and is analogous to polar-to-rectangularre-sampling that has been developed for spotlight Synthetic ApertureRadar (SAR). The projection operator, π, is computed as an operator thatsums values defined on the Generalized Bistatic Aperture along they-axis.

TAXO-R data for each delay-Doppler measurement cell is a set of vectorsamples, IQ, at 950.

This projection operator acts on both horizontal steering vectors 970and on weighted TAXO-R data 960 at 980. The projection operator is usedto deterministically reduce the dimensionality of both TAXO-R data and“horizontal” steering vectors.

The projected steering vector computed at 970 depends on the projectionoperator and the horizontal steering vector:πSV=π[ SV _(horiz)]

The weighted TAXO-R data at 960 is the element-by-element product ofvertical steering vectors and TAXO-R vector samples: SV _(vert)· IQ

The projected data is computed at 980 as the projection of weightedTAXO-R data:πX=π[ SV _(vert) · IQ]

An alternate mode of operation that can be realized with this embodimentis called Standard Bistatics with DBA Channel Sharing. For StandardBistatics with DBA Channel Sharing, the rotation angle computed at 910is set to zero. In this case, there is a simple one-to-onecorrespondence between transmitter and vertical steering vectors andanother simple one-to-one correspondence between receiver and horizontalsteering vectors.

For this alternate mode, Standard Bistatics with DBA Channel Sharing,horizontal and vertical steering vectors can be computed. For thisalternate mode, FIGS. 10 a-b and FIGS. 11 a-b show the characteristicsof example horizontal and vertical steering vectors.

FIG. 10 a shows the impulse response (IPR) for an example vertical ortransmitter steering vector displaced along the transmitter axis. TheIPR is computed as the vector dot produced between the example steeringvector and all steering vectors. The IPR is computed over the coordinategrid, GRID-SV_(φ=0), defined according to [000124]. FIG. 11 a shows thephase response of the example steering vector over the K_(tx)×K_(rx)DOF's in the Generalized Bistatic Aperture.

FIG. 10 b shows the IPR for a horizontal steering vector sample and FIG.11 b shows the corresponding phase response over the GeneralizedBistatic Aperture.

For the primary mode of operation employed by DBA, FIGS. 12 a-b andFIGS. 13 a-b show the characteristics of example horizontal and verticalsteering vectors. For this example, the transmitter and receiver speedsare the same. The displacements of transmitter and receiver DOF's arealso the same.

FIGS. 12 a-b show the displacement of the IPR for example vertical andhorizontal steering vectors over the coordinate grid, GRID−SV_(φ=0),defined according to [000128].

FIGS. 13 a-b show the phase response associated with each of the twosteering vector samples over the Generalized Bistatic Aperture.

The phase variation for the vertical steering vector in FIG. 13 a isentirely along the vertical axis. Similarly, the phase variation for thehorizontal steering vector in FIG. 13 b is entirely along the horizontalaxis

Because the phase for horizontal steering vectors is constant along theDOF's that are removed by the projection operator, application of theprojection operator to data weighted by a general steering vector can bedecomposed to projection of data weighted by a vertical steering vectorfollowed by weighting by a projected steering vector:π[ SV _(horiz) · SV _(vert) · IQ]=π[ SV _(horiz) ]·π[ SV _(vert) · IQ]

This establishes that the BAC Processor outputs, π[ SV _(horiz)] and π[SV _(vert)· IQ], provide a complete representation of the DBA data andsteering vectors. The BAC Processor outputs are passed to the ClutterMitigation Processor (CMP) where the projected data, π[ SV _(vert)· IQ],is adapted to projected steering vector, π[ SV _(horiz)].

A general steering vector can be formed as a product of vertical andhorizontal steering vectors. And, again in a similar manner, applicationof the projection operator to data weighted by a general steering vectorcan be factored into a product π[ SV _(horiz)]·π[ SV _(vert)· IQ]. Thefactor on the right is processed deterministically to reduce the DOF'sthat are to be processed adaptively.

Steering vectors are defined in terms of the gradient of the phase withrespect to the spatial and temporal DOF indices (k_(x), k_(y), n). Thegeneral steering vector for clutter consists of a 2-D vector thatrepresents the spatial components and a temporal component (a scalar):

$\overset{\_}{SV} \equiv \begin{pmatrix}{{\frac{d_{rx}}{\lambda}\cos\;(\beta){\sin\left( \theta_{rx} \right)}} + {\frac{d_{tx}}{\lambda}\sin\;(\beta)\sin\;\left( \theta_{tx} \right)} -} \\{{\frac{d_{rx}}{\lambda}\sin\;(\beta){\sin\left( \theta_{rx} \right)}} + {\frac{d_{tx}}{\lambda}\cos\;(\beta)\sin\;\left( \theta_{tx} \right)}}\end{pmatrix}$${SV}_{t} \equiv {{\frac{V_{rx}\delta\; t}{\lambda}{\sin\left( \theta_{rx} \right)}} + {\frac{V_{tx}\delta\; t}{\lambda}\sin\;\left( \theta_{tx} \right)}}$

The 3 dimensional space-time steering vector is:

${{\overset{\_}{SV}}_{3d} \equiv \begin{pmatrix}\overset{\_}{SV} \\{SV}_{t}\end{pmatrix}} = \begin{pmatrix}{SV}_{x} \\{SV}_{y} \\{SV}_{t}\end{pmatrix}$

The general, rotated spatial steering vector, SV, is:

$\overset{\_}{SV} \equiv \begin{pmatrix}{{\frac{d_{rx}}{\lambda}\cos\;(\beta){\sin\left( \theta_{rx} \right)}} + {\frac{d_{tx}}{\lambda}\sin\;(\beta)\sin\;\left( \theta_{tx} \right)} -} \\{{\frac{d_{rx}}{\lambda}\sin\;(\beta){\sin\left( \theta_{rx} \right)}} + {\frac{d_{tx}}{\lambda}\cos\;(\beta)\sin\;\left( \theta_{tx} \right)}}\end{pmatrix}$

In order to find appropriate transformations so that the set of steeringvectors for clutter are linear in the x-t plane (i.e., the projection ofstate vectors is a line in the x-t plane), the spatial steering vectorsare decomposed into bistatic clutter position vectors, X, bistaticsensor state vectors δ _(x), δ _(y), and ν (i.e., displacement andvelocity vectors) and rotation operators, M_(z)(β).

$\overset{\_}{SV} = {\begin{pmatrix}{\cos\;(\beta)} & {\sin(\beta)} \\{- {\sin(\beta)}} & {\cos(\beta)}\end{pmatrix}\begin{pmatrix}\frac{d_{rx}}{\lambda} & 0 \\0 & \frac{d_{tx}}{\lambda}\end{pmatrix}\begin{pmatrix}{\sin\left( \theta_{rx} \right)} \\{\sin\left( \theta_{tx} \right)}\end{pmatrix}}$where

The bistatic clutter position vector is:

$\overset{\_}{X} = {\begin{pmatrix}{\sin\left( \theta_{rx} \right)} \\{\sin\left( \theta_{tx} \right)}\end{pmatrix}.}$

The bistatic sensor state vectors are:

${{\overset{\_}{\delta}}_{x} = \begin{pmatrix}\frac{d_{rx}}{\lambda} \\0\end{pmatrix}},{{\overset{\_}{\delta}}_{y} = {{\begin{pmatrix}0 \\\frac{d_{tx}}{\lambda}\end{pmatrix}\mspace{11mu}{and}\mspace{14mu}\overset{\_}{\upsilon}} = {\begin{pmatrix}\frac{V_{rx}\delta\; t}{\lambda} \\\frac{V_{tx}\delta\; t}{\lambda}\end{pmatrix}.}}}$

The rotation operators are:

${M_{z}(\beta)} = {\begin{pmatrix}{\cos\;(\beta)} & {\sin(\beta)} \\{- {\sin(\beta)}} & {\cos(\beta)}\end{pmatrix}.}$

In more compact form, we can write:SV _(t) = ν ^(T) · XSV _(x) =[M _(z)(β)· δ _(x)]^(T) · XSV _(y) =[M _(z)(β)· δ _(y)]^(T) · X

We now choose the space-time rotation angle, β_(δγ), to ensure alignmentof the normalized displacement and velocity vectors:M _(z)(β)· δ _(x)=α ν

Equivalently, we require:

${\begin{pmatrix}{\cos\;(\beta)} \\{- {\sin(\beta)}}\end{pmatrix}d_{rx}} = {{\alpha\begin{pmatrix}V_{rx} \\V_{tx}\end{pmatrix}}T_{pri}}$

The solution is found as follows:

$\alpha = \frac{d_{rx}}{\sqrt{V_{rx}^{2} + V_{tx}^{2}} \cdot T_{pri}}$β_(δυ) = tan₂⁻¹(V_(tx), V_(rx))

The transformed space-time state vector is given by:

${SV}_{t} = {{\overset{\_}{\upsilon}}^{T} \cdot \overset{\_}{X}}$$\begin{matrix}{{SV}_{x} = {\frac{d_{rx}}{\sqrt{V_{rx}^{2} + V_{tx}^{2}} \cdot T_{pri}}\left( {{\overset{\_}{\upsilon}}^{T} \cdot \overset{\_}{X}} \right)}} \\{= {\frac{d_{rx}}{\sqrt{V_{rx}^{2} + V_{tx}^{2}} \cdot T_{pri}}{SV}_{t}}}\end{matrix}$ $\begin{matrix}{{SV}_{y} = {\left\lbrack {{M_{z}(\beta)} \cdot {\overset{\_}{\delta}}_{y}} \right\rbrack^{T} \cdot \overset{\_}{X}}} \\{= {{\frac{d_{tx}}{\lambda}\begin{bmatrix}{\sin\left( B_{\delta\upsilon} \right)} & {\cos\left( B_{\delta\upsilon} \right)}\end{bmatrix}}^{T} \cdot \overset{\_}{X}}}\end{matrix}$

This establishes that the clutter state vectors are constrained to liein a plane. The normal to the plane is:

$\hat{n} = {\sqrt{\frac{\left( {V_{rx}^{2} + V_{tx}^{2}} \right) \cdot T_{pri}^{2}}{{\left( {V_{rx}^{2} + V_{tx}^{2}} \right) \cdot T_{pri}^{2}} + d_{rx}^{2}}}{\left\{ {{\frac{d_{rx}}{\sqrt{V_{rx}^{2} + V_{tx}^{2}} \cdot T_{pri}}{\hat{e}}_{t}} - {\hat{e}}_{x}} \right\}.}}$

The 2-dimensional plane of clutter state vectors is spanned by aspace-time vector, {circumflex over (ω)}_(st), and a purely spatialvector, {circumflex over (ω)}_(sp), where:

${\hat{\omega}}_{st} = {\sqrt{\frac{\left( {V_{rx}^{2} + V_{tx}^{2}} \right) \cdot T_{pri}^{2}}{{\left( {V_{rx}^{2} + V_{tx}^{2}} \right) \cdot T_{pri}^{2}} + d_{rx}^{2}}}\left\{ {{\hat{e}}_{t} + {\frac{d_{rx}}{\sqrt{V_{rx}^{2} + V_{tx}^{2}} \cdot T_{pri}}{\hat{e}}_{x}}} \right\}}$and ω̂_(sp) = ê_(y)

The projection operator, π=Ĩ−ω_(sp){circle around (×)}ω_(sp) transformsthe clutter locus from a plane (or set of parallel planes) in a3-dimensional into a line (or set of planes lines) in a 2-dimensionalspace. The projection operator is computed as a function of the identityoperator, Ĩ, and spatial basis vector for the plane of clutter statevectors, {circumflex over (ω)}_(sp). {circle around (×)} denotes theouter product. After projection, clutter measurements are constrained toa 1-dimensional sub-space. The space-time vector, {circumflex over(ω)}_(st), provides a basis for this 1-dimensional sub-space of clutterstate vectors.

This explicitly demonstrates the desired linearity of transformedclutter state vectors.

Before projection, the clutter locus for clutter samples with a commondelay measurement are a subset of the 2-dimensional plane. Thespace-time vector, {circumflex over (ω)}_(st), describes the1-dimensional clutter locus after projection. This explicitlydemonstrates that the linearity of the clutter state vectors afterprojection is delay-independent. The delay independence ensures thatstatistical characterization of clutter properties based on data inneighboring delay strips will approximate the statistical behaviour onany delay strip selected for clutter suppression and target detection.In this manner, desirable features of monostatic radar operation onmoving platforms in a clutter environment are realized by thisinvention.

The clutter state vectors characterize the clutter covariance and thelinearity of the projected clutter state vectors ensure that the cluttercovariance is reduced rank. The delay independence of the clutter statevectors ensure that sample matrix techniques accurately estimate thereduced rank clutter covariance.

For ambiguous measurements, the temporal component of the clutter statevector, SV_(t), is modified by the addition of a constant term. Thisleads to an additional plane of clutter measurements that is parallel tothe primary plane of measurements. In general, clutter state vectorswill span a set of parallel planes.

FIG. 14 shows a block diagram for an example Clutter MitigationProcessor (CMP) 140 that may be integrated with the DBA Pre-processor(TAXO-R+BAC). FIG. 14 shows an input of N data channels 142 (eachconsisting of K_(rx) receiver channels) with each succeeding channeldelayed by an additional dn pulses 144. The architecture is designed tosupport a technique called Staggered PRF, a specific form ofPost-Doppler STAP.

The Format STAP DataCube 148 block populates a 3-dimensional data arraywith data that represents spatial DOF's (projected data at the output ofthe BAC processor) 146, slow-time DOF's (derived from the staggered datastreams) and fast-time DOF's (derived from neighboring delay strips).The formatting process for data and for SV's re-organizes themulti-dimensional array into a single vector.

The DataCubes, X(m,n), are parameterized by delay and Doppler indices, mand n. The Estimate Inverse Covariance block 150 computes the covarianceof each DataCube:{tilde over (R)}(m,n)= X (m,n)· X (m,n)^(T)

An estimate of the covariance at a delay-Doppler sample (with indices m₀and n₀) is computed as an average of {tilde over (R)}(m,n₀) overneighboring delay bins:

${{\overset{\sim}{R}}_{est}\left( {m_{0},n_{0}} \right)} = {\frac{1}{2N_{R}}{\sum\limits_{\underset{m \neq m_{0}}{m = {m_{0} - N_{R}}}}^{m_{0} + N_{R}}{\overset{\sim}{R}\left( {m,n_{0}} \right)}}}$

The number of samples used to compute the estimated covariance is N_(R)which is chosen to be on the order of the number of DOF's (i.e., thelength of the vector X).

For each delay-Doppler sample, the eigenvectors, ū_(q)(m₀,n₀), andeigenvalues λ_(q)(m₀,n₀) of {tilde over (R)}_(est)(m₀, n₀) are computed.

The principal components estimate of the inverse covariance begins withan exact expression for the inverse:

${R_{est}\left( {m_{0},n_{0}} \right)}^{- 1} = {\frac{1}{\lambda_{\min}}\left( {\overset{\sim}{I} - {\sum\limits_{q = 1}^{N}{\left( \frac{{\lambda_{q}\left( {m_{0},n_{0}} \right)} - \lambda_{\min}}{\lambda_{q}\left( {m_{0},n_{0}} \right)} \right){{\overset{\_}{u}}_{q}\left( {m_{0},n_{0}} \right)}{{\overset{\_}{u}}_{q}\left( {m_{0},n_{0}} \right)}^{\prime}}}} \right)}$

The minimum eigenvalue, λ_(min) will typically be set by noise and theprincipal components technique restricts the summation to thoseeigenvalues that exceed the minimum eigenvalue by a pre-set threshold.

The Compute STAP Weights block 152 applies the estimated inversecovariance to the projected steering vector:W _(proj)(m ₀ ,n ₀)={tilde over (R)} _(est)(m ₀ ,n ₀)⁻¹ SV _(proj)

The Filter STAP Data block 154 applies the weights to the STAP DataCube:Y (m ₀ ,n ₀)= W _(proj)(m ₀ ,n ₀)′· X (m ₀ ,n ₀)

The Clutter Mitigation Processor shown in FIG. 14 and integrated withthe embodiment of BAC shown in FIG. 9 comprises a two-stage DBA clutterprocessor. The DBA clutter processor operates on Data Quads and iscalled Projected Bistatic STAP. FIG. 15 a shows the SINR Loss over thespace-time aperture for the same example airborne bistatic radarsimulation. The offset of logarithmic scale in FIG. 15 a has been setarbitrarily to coincide with FIG. 15 b. The minimum value corresponds toa SINR Loss of −40 dB. The region of high SINR Loss and a high value ofclutter suppression is called the clutter null and coincides with thelinear clutter locus for that scenario. Regions in the space-timeaperture away from the clutter null show a lower level of signalsuppression that approaches the value of the scale which corresponds toa SINR Loss that is near 0. Targets with angle-Doppler measurements inthis region of the space-time aperture will be attenuated by an amountthat is measurably less than the attenuation of clutter. In this regard,this invention is said to linearize and localize the clutter null and tominimize the MDV.

DBA technology can be integrated with a broad classes of adaptive andnon-adaptive clutter mitigation techniques including STAP with orwithout derivative-based updating and with or without Doppler-anglecompensation. The current embodiment represents one example.

The current embodiment of Projected Bistatic STAP operates on3-dimensional subspaces of the Data Quads. The 3-dimensional subspacesare defined by transmitter DOF's, receiver DOF's and temporal DOF's. Thefirst stage of the current embodiment uses non-adaptive processing toexploit the reduced clutter rank and to reduce the subspace from3-dimensions to 2-dimensions. The second stage applies adaptiveprocessing to the residual 2-dimensional sub-space. An alternateimplementation combines BAC and clutter mitigation processing into asingle stage algorithm that applies adaptive processing to the full3-dimensional subspace. MWF provides an example algorithm that operatesdirectly on data in the Generalized Bistatic Aperture and integrates theclutter rank reduction realized separately by BAC and CMP for thecurrent embodiment.

An alternate embodiment is called Electronic Clutter Tuning. ElectronicClutter Tuning replaces the adaptive CMP with a non-adaptive processor.The non-adaptive processor is comprised by the direct, non-adaptiveapplication of generalized steering vectors to the output of the BACprocessor. Electronic Clutter Tuning, is designed to reduce thedimensionality of the clutter and expand the volume of measurement spacethat can be used for target detection. FIG. 15 b shows the SINR over thespace-time aperture for an example airborne bistatic radar simulation.FIG. 15 b shows the compression of the interference due to clutter to aregion that coincides with the linear clutter locus for the scenario.The compression of the clutter is similar in concept to traditionalclutter tuning approaches, but is accomplished without any constraintson bistatic platform motion. The logarithmic scale in FIG. 15 a providesa direct measure of SINR. FIG. 15 b demonstrates the improvement inbistatic radar performance without the application of STAP or otherclutter mitigation processing that is obtained with this invention.

An alternate embodiment is called the Distributed Bistatic Beamformer.The Distributed Bistatic Beamformer is comprised by the direct,non-adaptive application steering vectors to the TAXO-R output. Theoutput of the Distributed Bistatic Beamformer is a 4-dimensional arrayof measurements. The 4-dimensional array is spanned by a temporal2-dimensional sub-space and a spatial 2-dimensional sub-space.Measurements in the 2-dimensional temporal sub-space correspond to delayand Doppler or delay and slow-time. Measurements in the 2-dimensionalspatial sub-space correspond to transmitter and receiver anglemeasurements. The 2-dimensional sub-space for a selected delay-Doppleror delay-time measurement is called the Characteristic BistaticAperture. For the current embodiment, the Characteristic BistaticAperture provides simultaneous unbiased angle measurements of cluttersources relative to the transmitter and relative to the receiver.

The foregoing description of the preferred embodiment of the inventionhas been presented for purposes of illustration and description. It isnot intended to be exhaustive or to limit the invention to the preciseform disclosed, and modifications and variations are possible in lightof the above teachings or may be acquired from practice of theinvention. The embodiments were chosen and described in order to explainthe principles of the invention and its practical application to enableone skilled in the art to utilize the invention in various embodimentsas are suited to the particular use contemplated. It is intended thatthe scope of the invention be defined by the claims appended hereto, andtheir equivalents. The entirety of each of the aforementioned documentsis incorporated by reference herein.

1. A method of filtering and processing a received radar signalcomprising the steps of: receiving an element-level radar signal;splitting said element-level radar signal into a plurality of signalcomponents, each said signal component comprising energy scattered by aspecific transmit element—receiver—element pair; forming a 2-D array ofdata associated with a plurality of transmitter and receiver degrees offreedom; rotating said 2-D array of data; re-sampling said array of datato find new degrees of freedom; and using a projection to eliminateresidual degrees of freedom.
 2. A method of filtering and processing areceived radar signal comprising the steps of: receiving anelement-level radar signal; splitting said element-level signal into aplurality of signal components, each said signal component comprisingenergy scattered by a specific transmitter element—receiver elementpair; generating a Complex Ambiguity Function by filtering saidplurality of signal components, each filtered signal componentcomprising energy delayed by a specific value and Doppler shifted by aspecific value relative to the direct path signal; generating aplurality of 4-dimensional labels for components of signal energy; andperforming Reduced Rank STAP processing on said filtered signalcomponents.
 3. A method of filtering and processing a received radarsignal comprising the steps of receiving an element level radar signal;generating a Complex Ambiguity Function by filtering said element-levelradar signal into a first plurality of signal components, each of saidfirst plurality of signal components comprising energy delayed by aspecific value and Doppler shifted by a specific value relative to thedirect path signal; filtering said Complex Ambiguity Function into asecond plurality of signal components, each of said second plurality ofsignal components comprising energy scattered by a specific transmitelement and received by a specific receiver element; generating aplurality of 4-dimensional labels for components of signal energy; andperforming Reduced Rank STAP processing.